提出在散射介质中实现色彩恢复唯一解的充分条件。
Conditions for well-posed color recovery in scattering media
- 基于光谱信号投影与介质参数未知性，构建可解框架
- 理想高光谱相机下恢复结果唯一，误差可控
- 适合光学成像、逆问题求解研究者参考
从散射介质中捕获的图像恢复场景色彩是光学成像中的基础逆问题。然而该问题本质上是病态的，因为多个解可能解释同一观测结果，且在不了解候选解空间的情况下无法控制预测误差。本文提出了在散射介质中色彩恢复成为适定问题的充分条件。我们发现病态性源于（i）光谱信号向像素强度的投影，以及（ii）介质参数未知。证明仅靠传感器改进无法消除介质引起的失真，除非引入额外约束。通过识别图像中自然存在的跨像素关系模式，我们证明对于理想高光谱相机，这些关系将解空间压缩至唯一候选解。这为基于第一性原理的新一代视觉算法打开通道，使散射环境下的图像定量分析成为可能。
原文摘要 · Abstract (English)
Recovering scene color from images captured in scattering media is a fundamental inverse problem in optical imaging. Yet the problem is intrinsically ill-posed as multiple solutions can explain the same observation, and prediction error cannot be controlled without understanding the space of candidate solutions. Here, we present sufficient conditions under which color recovery in a scattering medium becomes well-posed. Observing that ill-posedness stems from (i) projection of spectral signals onto pixel intensities, and (ii) unknown medium parameters, we demonstrate that sensor improvements alone cannot resolve medium-induced distortions without additional constraints. We identify recovery patterns, cross-pixel relationships that naturally occur in images, and prove, for an ideal hyperspectral camera, that they restrict the solution to a unique candidate. This opens the door to a new class of vision algorithms grounded in first principles, enabling quantitative analysis of images in scattering environments.
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